Two day mini-course
Prof. JP Anker (Orleans): An overview of Fourier analysis related to root systems
Day 1: 14 May 2015, 14:00-16:30, Huxley 139
Fourier analysis on symmetric spaces and affine buildings was built up during the second half of the 20th century, mainly by Harish-Chandra, Helgason and Macdonald. Nowadays it has given birth to a far reaching theory of special functions in several variables related to root systems, developed by Cherednik, Dunkl, Heckman, Macdonald, Opdam, Rösler, … and often referred to as Dunkl theory. In these two lectures we shall start with classical radial Fourier analysis on Euclidean spaces, hyperbolic spaces and homogeneous trees, move on to Jacobi functions, and gradually to Dunkl theory in dimension 1 and higher. If times permits, I will discuss applications to some evolution equations such as the heat equation, the Schrödinger equation or the wave equation.
Day 2: 15 May 2015, 14:00-16:30, Huxley 130
Abstract as above.